Question: Solve for $a$, $ -\dfrac{3}{a} = \dfrac{5}{4a} + \dfrac{4a - 5}{a} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $a$ $4a$ and $a$ The common denominator is $4a$ To get $4a$ in the denominator of the first term, multiply it by $\frac{4}{4}$ $ -\dfrac{3}{a} \times \dfrac{4}{4} = -\dfrac{12}{4a} $ The denominator of the second term is already $4a$ , so we don't need to change it. To get $4a$ in the denominator of the third term, multiply it by $\frac{4}{4}$ $ \dfrac{4a - 5}{a} \times \dfrac{4}{4} = \dfrac{16a - 20}{4a} $ This give us: $ -\dfrac{12}{4a} = \dfrac{5}{4a} + \dfrac{16a - 20}{4a} $ If we multiply both sides of the equation by $4a$ , we get: $ -12 = 5 + 16a - 20$ $ -12 = 16a - 15$ $ 3 = 16a $ $ a = \dfrac{3}{16}$